Who else would like to see more wide cams on the market?

All clear now. Thanks. I've been able to replicate the numbers and the graph.

Cool. Thinking on it more last night I think the disconnect was that I'm looking at the expansion linearly rather than logarithmically, which means the rotation per unit goes down as the rotation increases. Or to put it another way, I see where you're coming from. Hopefully the blue graph above makes sense now, given the screwy-small amount of rotation it needs to get the same amount of linear expansion as the earlier sections of the curve.

Ok, back to work on the dual-axle program. Anyone have an idea what I was using the Delta variable to track? Been staring at it for hours, and frankly have no idea what it was for since it was zeroed out later on.

Sigh. I need to learn to document better, as while I never expected to let the program sit for 2 years, that's exactly what happened. I seem to recall it having something to do with half the axle diameter plus clearance of the tip of the lobe on the opposite wall plus the amount of material left on the lobe around the axle, but don't remember why that was important.

Crap.

A question:

Why do you need larger dia axle(s)? Is this because the head width will be increased?

I'm interested in acquiring one, assuming double axle and a range that runs roughly 5.5 - 9.1

Basically I'd like to see the added range partially on the small end (i.e. it goes a little tighter than 5.7) rather than solely on the wide end.

Do you have a ballpark estimate for finished production?

Will S wrote:A question: Why do you need larger dia axle(s)?

It's not so much 'need' as 'want'... One of the prime failure modes for big cams is buckling of the lobes, and I think a larger diameter axle will go a long way towards reducing the lever arm that causes the buckling.

Will S wrote: Do you have a ballpark estimate for finished production?

I believe I said a while back they'd be the same as Tom charges for a 9 VG. Once I firm up the design I'll have a better idea of the costs and will give a hard price then.

Interesting. Changing the lever arm, at most say 1/2" over a ~5" span, call it 10%, will be effective in reducing the propensity to buckle?

I meant estimated timeline, not cost.

Aric -
Since the one I built is somewhat similar to this idea, I could probably convince Wally to let you borrow it for a while if it would help you work out your design (learn from what I got right/wrong.) And/or I can send you my CAD files if that might help.

Will S wrote:Interesting. Changing the lever arm, at most say 1/2" over a ~5" span, call it 10%, will be effective in reducing the propensity to buckle?

Dunno, that will shake out as the design is finalized. FWIW, I'm mostly thinking along those lines for a single axle, not double, since the double can have the lobes supported by the plates on the end terminations.

Will S wrote: I meant estimated timeline, not cost.

Oops. Gotcha. Short answer: not terribly soon and if you're in a hurry give Tom@VG a call. I figure it'll take a couple iterations to get everyone on board on a design, followed by making and breaking a sample or two, revising, another sample or two and then running a batch of final version. I'm currently tied up with finishing renovations on a circa 1850 schoolhouse we bought last year, so don't have much free time for anything beyond design/modeling until that's done (at the moment what little free time I have is spent with my wife&toddler, and design/modeling I can do while they watch a movie). I figure I'll be done with that project in the next 4-6 weeks, at which point my schedule gets a lot more flexible. So maybe year end?

EDIT- I realize "year end" might sound like a long time out, but frankly I've got my plate more than full at the moment and am only getting into this big cam stuff as a favor to those wanting other options, as I need a break from the house renovation and want to rejuvenate my interest in machining so I can finish off the line of cams I've had out for beta testing for the past year or so. Not interested in a wait, give Tom a call. Don't mind waiting, post up what you'd like and we'll see what we can get a group of folks to agree upon. A few folks here have seen the quality of my work (the aforementioned cams in beta test), but unfortunately the most vocal of the bunch recently left MP so I'm lacking references at the moment.

Quick bump to say I've been pondering this project in what little free time I've had and have the dual-axle springing worked out (issue being wanting to better support the lobes for sideways loading than is done in currently-available cams). Looks like I'm on baby-sitting duty the next two weeks, so provided she naps I'll finally have a chunk of time each day to work on this. The program to calculate the optimized increasing-cam-angle curves is ~80% finished (working for single axle), so looking forward to getting this project moving.

will update as there's news....

-a.

Lots or progress this week thanks to the babysitter being out of town (and me being home instead of working), and it looks like I have the combined/generalized program working (previously had separate programs for single and double axle cams). Need to play with it a bunch more to make sure it's working properly, but it's looking good so far.

So, here's something to chew on for a couple days while I take a break from programming.... I'm not sold on this increasing-cam-angle thing, so will throw it out here for discussion.

In a nutshell, I ran several scenarios with is using curves with a base 14 degree cam angle and limited the increase such that it would be ~15 degree cam angle at 60% expansion and below 18 degree cam angle at the tip, figuring allowing the cam angle to run up at the end would gain range at the expense of holding power. Turns out that the additional range over simply using a constant 15 degree cam angle was negligible, hence me not being sold on the idea. Thing is, those are limiting values I picked kind of arbitrarily and the increase would be much greater if those limitations were loosened up (like letting it run up higher in the middle of the expansion and say, 20+ degrees at the tip). Dunno if I'm thrilled with that idea, but figured I'd throw it out for discussion.

To help make it clearer, here are some graphs and charts of the results:

First up, single axle cam to fit into a 100mm crack. The red curve has a constant 14 degree cam angle, the orange curve a 15 degree cam angle, and a blue one that increases from 14.1 degrees to just under 18 degrees at the tip (the exact cam angles for every 10% of expansion are in the results).

Here are the numbers for it: (Click to enlarge it so it's readable, red arrow is the max range, green arrow the cam angle and orange the overall range and expansion ratio)


Second is a set of double axle cams for a 100mm crack, again with the red curve having a constant 14 degree cam angle, the orange curve a constant 15 degree cam angle and the blue one with an increasing cam angle.



And the numbers:


I'm going to ponder this for a couple days, but please feel free to chime in with your thoughts.

-a.

1.5 cm more range for a double axle cam seems non-trivial to me in this size. I'm just imagining what a large double-axle U-stem cam might look like. Could use some fun equalization system for the two cables or something...

Hmmm.. Replied to this a while ago and it's nowhere to be seen.

Anyway, sorry for the confusion... It's going to be double axle; I just included the single axle chart/results because I thought it interesting how the increasing angle thing worked similarly in either case (which differs from the earlier analysis).

I haven't look at a force v. cam angle diagram in a long time, but my recollection is that using the common coeffcient of friction for rock/aluminum at about 0.35, anything beyond about 18deg is getting pretty sketchy and at 20deg you've reached critical point.

I wouldn't personally use a cam above 18deg. Isn't the Alien design about 17?

I have a design in my head for a large cam that probably infringes on a number of patents. 3 lobes, an offset loading point on the one lobe, kind of like Max cams but without the 3 axles. A complete 360 degree spiral like the Super cam, and a hook that can flip everything around to hook behind flakes like that flake grabbing thing that guy cobbled together, but only have one set of cams on the outside.

Here's a quick idea of what I mean. Nothing is necessarily to scale. I think it should be able to get about 2:1 range. No idea if the flake pinching part would work out. It would require a lot of rotation and torque on the lobe.

Too many spirals in my figure, but the bottom line is that it agrees with the one posted above.

• The red line has constant 14 degree pitch
• The green line has constant 15 degree pitch
• The blue line has linearly increasing pitch starting at 14.1 and going up to 17.85
• The cyan line has polynomial pitch starting at 14.1 and ending at 17.89 such that the pitch at the 60% expansion point is still below 15 degrees

Hey Brenta- been on the fence about publishing the equation I'm using, but if it saves you some trouble I can forward you the equation and/or Mathematica program. Thx for double checking my work, btw. Seriously. Been staring at this stuff way too long, and all too easy to miss something stupid. :-)

This is my script; it works with both Matlab and Octave. I have a more efficient version, which uses closed-form solutions for the differential equations in three of the four cases, but it's messy and efficiency doesn't matter much for this problem.

-------------------------------------------
clear, clf
% Useful constants.
crackWidth = 100;
minRadius = crackWidth / 2;
numPoints = 1000; % for plotting

% Anonymous function handles for generic spirals. All these spirals are
% described by dr/r = tan(pitch(theta)) dtheta. Pitch is a polynomial in theta.
% If the polynomial is a constant, the curve is a logarithmic spiral.

pitch = @(coeff) @(theta) polyval(coeff,theta);
spiral = @(r0,pitch,theta0) @(theta) r0*exp(arrayfun(@(x) quad(@(t) tan(pitch(t)),theta0,x),theta));

% Define curves to be plotted.
spirals(1).color = 'r'; % red
spirals(1).coeff = [14*pi/180];
spirals(1).plot = true;

spirals(2).color = 'm'; % magenta (used to be green)
spirals(2).coeff = [15*pi/180];
spirals(2).plot = true;

spirals(3).color = 'b'; % blue
spirals(3).coeff = [1/33 14.1*pi/180];
spirals(3).plot = true;

spirals(4).color = 'c'; % cyan
spirals(4).coeff = polyfit([0 pi/6 pi/4 pi/2 2*pi/3], [14.1 14.2 14.3 15 17.2]*pi/180, 4);
spirals(4).plot = true;

% Compute details for each curve.
for i=1:length(spirals)
  if spirals(i).plot
    spirals(i).pitch = pitch(spirals(i).coeff);
    % Compute the rotation required to fit the cam in the crack,
    % whose width is twice the minimum radius.
    tmpfun = spiral(1,spirals(i).pitch,0);
    spirals(i).phi = fsolve(@(theta) tmpfun(theta) - 1/cos(spirals(i).pitch(theta)), 0.1);
    spirals(i).theta0 = spirals(i).pitch(spirals(i).phi) - spirals(i).phi;
    fprintf('theta0 %s = %g degrees\n', spirals(i).color, spirals(i).theta0*180/pi);
    % Get the specific spiral.
    spirals(i).curve = spiral(minRadius,spirals(i).pitch,spirals(i).theta0);
    % Compute the final angle.
    spirals(i).finalAngle = fsolve(@(theta) spirals(i).curve(theta) .* cos(theta) + minRadius, 0.7*pi);
    fprintf('final angle %s = %g degrees\n', spirals(i).color, spirals(i).finalAngle*180/pi);
    spirals(i).maxRadius = spirals(i).curve(spirals(i).finalAngle);
    % Compute range. The factor of 2 accounts for the two opposing lobes.
    spirals(i).range = 2 * (spirals(i).maxRadius * cos(spirals(i).pitch(spirals(i).finalAngle)) - minRadius);
    fprintf('range %s = %g mm\n', spirals(i).color, spirals(i).range);
    % Percentages of range.
    spirals(i).pr = zeros(10,1);
    for j=1:10
      spirals(i).pr(j) = fsolve(@(theta) spirals(i).curve(theta) .* cos(spirals(i).pitch(theta)) ...
        - minRadius - j * spirals(i).range / 20.0, 1);
    end
  end
end

% Plot
hold on
for i=1:length(spirals)
  if spirals(i).plot
    spirals(i).t = linspace(spirals(i).theta0,spirals(i).finalAngle,numPoints);
    spirals(i).handle = polar(spirals(i).t, spirals(i).curve(spirals(i).t));
    set(spirals(i).handle,'color',spirals(i).color,'linewidth',2);
    plot([0 minRadius*cos(spirals(i).theta0)], [0 minRadius*sin(spirals(i).theta0)], ...
      spirals(i).color, 'linewidth', 2);
    plot([0 spirals(i).maxRadius*cos(spirals(i).finalAngle)], ...
      [0 spirals(i).maxRadius*sin(spirals(i).finalAngle)], ...
      spirals(i).color, 'linewidth', 2);
    plot([0 spirals(i).curve(spirals(i).pitch(spirals(i).phi))*cos(spirals(i).pitch(spirals(i).phi))], ...
      [0 spirals(i).curve(spirals(i).pitch(spirals(i).phi))*sin(spirals(i).pitch(spirals(i).phi))], ...
      spirals(i).color, 'linewidth', 1);
    for j=1:10
      plot([0 spirals(i).curve(spirals(i).pr(j))*cos(spirals(i).pr(j))], ...
        [0 spirals(i).curve(spirals(i).pr(j))*sin(spirals(i).pr(j))], ...
        spirals(i).color, 'linewidth', 1);
    end
  end
end

xlim([-52 52]);
ylim([0 82]);
line([50,50], ylim);
line([-50,-50], ylim);
axis('equal')
hold off

Crap. Had a long explanation of where this project is, and the combination of exhaustion and drooping thumbs on a laptop with touchpad lead to losing the whole thing.

Sigh.

Short version:

Thanks for posting your program Brenta. Seeing that, I'm embarrassed to post mine... Clearly I've not even stayed in a Holiday Inn Express, given how ugly my program is. But it does what I need it to do, so all is well I guess.

Key bit I was talking about is this... the equation I'm using for the curve is along the lines of: (sorry about the lack or reformatting... its hours past when I should have been in bed)

reg[\[Theta]_] = areg*Exp[Tan[\[Theta]reg]*\[Theta] + b*\[Theta]^c + d*\[Theta]^e]

where:

areg = the minimum size crack the piece can fit, taking into account single or double axle and the axle spacing

[theta]reg = the tangent angle of the curve

b = first modifier

c = first exponential modifier

d = second modifier

e = second exponential modifier

In a nutshell, it's not much different from what I heard was done with the SuperCam (with its second order modifier), but with a slight twist that allows the curve to grow within acceptable tan angles within normal rotation (like what I surmise happens with the SuperCam), and then shoot outwards in the last final bit of rotation. IIRC the formula for the plot I posted earlier was something along the lines of:

reg[\[Theta]_] = areg*Exp[Tan[14Deg]*\[Theta] +0.005*\[Theta]^2 + 0.0005*\[Theta]^6]

Sadly, after playing with this for longer that I'd like to admit I don't think there's any benefit from going this route for typical single and dual axle designs, as any gains on the tail end are easily met by simply upping the tangent angle a small amount for a regular log spiral (which leads to the usual Metolius vs BD debate). I've not looked at the implications of what happens with large amounts or rotation, so perhaps this is what lets the SuperCam do its magic. Dunno, and frankly have little interest in pursuing this train of though further unless someone chimes in with a compelling reason to do so.

So, any thoughts?

On a side note, I've been on babysitting duty the past 2 weeks, which means naptime has been spent finally reorganizing the workshop to fit the "new" lathe (1970's vintage Clausing 5900). Which in turn means I'm a big step towards having the milling machine back operational, which means this project is closer to moving forward. Which means anyone with an opinion about what they'd like better start chiming in, otherwise Killis is apparently running the show.

If you are making a large cam with a large hollow axle, then you should ditch the stem completely. Spread the lobes far enough apart that you can fit your fist in the middle. This will increase the torque a bit, but an oversized axle should be able to handle it. The trigger can be a bar and curved slot through the lobes that you simple grab and squeeze. This saves weight and volume, and in my opinion, would make it easier to handle and place.

If you want to get extra range, load off the backside of one of the lobes instead of the axle. It's the same principle as the Max Cams (only one pair is offset) and Totem Cams (all lobes get an offset loading). Or do a complete spiral like the Super Cam. Or do both.

All Killer No Filler wrote:I'm running nothing, I'm just up for chipping in so you can push the design envelope.

True, but you seem to be the only one chiming in, so by default you're in charge... :-)

Been cogitating on Danny's suggestion above re: MaxCam-esque design, and am going to pass on that. I've been sitting on what I think would be a solution to the MaxCam flop issue for a while now (really have to get around to cutting one of my #2's apart to try it...), but my solution won't play well with widely spaced lobes on large sizes due to side loading of the inner lobes.

Anyone have any comments re: the increasing cam angle stuff I posted above? Specifically, which would you prefer: a constant 15 deg cam angle or one that increases from 14 to 15 in the normal usable range (66% expansion) and then jumps up to ~18 deg or so for the last bit? Looks to me that there's no advantage to the increasing angle thing range-wise, but it would give relatively more holding power in the usable range.

-a.

The flop issue is only because the stem and trigger were up at the offset axle. If you stick with a single axle it's fine. If you simply load a long sling off the back of two of the lobes so that they are equalized, you get very little side load (long sling = less side pull). If you still think it is too much, it would be very simple to add a spreader bar to the sling, to keep it from pulling the lobes together.